Key Physics Topics for Plasma Wakefield Accelerator Research Topics for Plasma Wakefield R&D at FACET and Beyond It is a great pleasure and honor to open the 2005 meeting of the APS DPP with a talk on Plasma Accelerators. There has been remarkable progress made in the past 1-2 years by several groups around the world, and I am delighted to be able to share some of the exciting results with you. The movie you have been enjoying in the background of this title is courtesy of Frank Tsung . It is a simulation of a laser WFA and you can see a beam emerging from the plasma in this image of plasma density isocontours. W.B.Mori University of California at Los Angeles Much is based on QuickPIC and OSIRIS Simulations Doe FACET Review February 19, 2008

Key Physics follows from energy gain and beam quality considerations Energy Gain=eEloaded x Lacc eEloaded= Gradient of Loaded wake Wakefield amplitude (accelerating and focusing fields) Beam loading Lacc= acceleration length Ldephasing Not an issue for PWFA Lpumpdepletion High Transformer Ratios Ldiffraction Head Erosion Linstability Hosing Uncompensated Nonlinear Focusing forces leads to Emittance growth after several betatron periods (effective area increased) x px sx Plasma focusing causes beam to rotate in phase space Radially dependent accelerating field leads to energy spread But by far the most demanding requirements on accels are for HEP HE -- at least 125 GeV on 125 GeV to discover the Higgs

Wake excitation Narrow beams

Blowout or Bubble regime for PWFA Rosenzweig et al. 1990, Lu et al. 2006 Trajectory crossing Ion channel formed by trajectory crossing Ideal linear focusing force Uniform acceleration Fluid model breaks down! 2D/3D and electromagnetic in nature! Driven by an electron beam What do we want to know and predict? Wake excitation for given drive beam …… Evolution of drive beam, e.g, instabilities… Transformer ratio, shaped bunches, train of bunches Beam loading, beam quality …… How to put these all together in a design? What about positrons? Driven by a laser pulse

Wakefields are completely characterized by the trajectory of the blowout radius W. Lu et al., Phys. Rev. Lett. 16, 16500 (2006) The trajectory of the inner most particle is Space charge of beam Ponderomotive force of laser Two distinct limits: Ultra-relativistic blowout (behind the driver) Non-relativistic blowout Nearly a circle!

Uniform accelerating field Field structure in blowout regime Relativistic blowout regime for blowout radius Lu et al.PRL 16, 16500 [2006] Bubble radius : Uniform accelerating field Linear focusing field

Beam Loading linear regime In the linear regime one superimposes the wake by trailer to the wake by the driver to find the total wakefield [1]. Bunch shaping for no energy spread: Triangular. The total charge can be found by requiring that all of the energy in the wake is absorbed. [1] T. Katsouleas, S. Wilks, P. Chen, J. M. Dawson, J. J. Su - Part. Accel, 1987

Original simulation results: 1987 Drive beam (laser or particle beam) Note that wedge gives nearly constant decelerating field Properly phased trailing beam of particles: Loads wake In linear theory just use superposition: Add wakes => (for spot size c/wp) 100% energy extraction (though Vgr=0) 100% energy spread Katsouleas, Wilks et al., 1987

Nonlinear beam loading: Solve equation for Rb(x) M Nonlinear beam loading: Solve equation for Rb(x) M. Tzoufras, in preparation These equations are integrated for a trapezoidal () to obtain Ez() and rb(). This allows us to design accelerators with 100% beam-loading efficiency that conserve the energy spread.

Nonlinear beam loading M. Tzoufras, to be submitted Nonlinear beam loading theory has been confirmed in fully nonlinear particle-in-cell simulations Blue arrow is from ions Green arrows is from beam Black arrows is the trajectory

25 GeV Stage No energy spread 25 GeV Driver 25 GeV Trailing beam he ion motion run has the same parameters as the 25gev run except the initial energy of 250GeV. The run was done with 2048x2048x256 cells, and with 0.01 c/wp resolution in transverse direction and 0.047 c/wp in the longitudinal direction. 4 particle/cell is used. The max compression is 217 n_p, the second plot in that slides is actually blown up from the first plot. 25 GeV Driver 25 GeV Trailing beam 25 GeV Driver 475 GeV Trailing beam np=5.661016cm-3 Ndriver = 4.421010, r= 3 m, L = 58 m, Energy = 25 GeV Ntrailing = 1.71010 , r= 3 m , L = 22 m, Energy = 25 GeV or 475 GeV Rtrans = -Eacc/Edec = 1

Pump depletion: Transformer ratio

Can the transformer ratio be increased. W Can the transformer ratio be increased? W.Lu PhD Dissertation UCLA 2007 Linear theory: Triangular or wedge shaped bunch + precursor leads to constant E_ and an E+ that Nonlinear blowout regime: - Starting from equation of Lu et al., it can be shown that the optimal shape of a single bunch is once again a wedge (but without the need for a precursor np=21016cm-3 Ndriver = 21010, r= 3 m, L = 390 m Ntrailing = 0.67109 , r= 1 m, L = 15 m Edec= 0.085 mcp/e Eacc= -0.85 mcp/e Rtrans= -Eacc / Edec = 10

High transformer ratio used a wedge shaped beam Blowout regime flattens wake, reduces energy spread Beam load Ez Unloaded wake Loaded wake Nload~30% Nmax 1% energy spread

Multi-bunch Afterburner Drivers: 75pC*(1:3:5:7)~1nC Witness: 0.3/R*1nC~50pC Transf. Ratio ~ 7 Transformer Efficiency ~ 30% Themos Kallos, USC

Hosing (Head-tail) Instability Caused by the coupling between the beam and the electron sheath at the ion channel boundary. Triggered by head-tail offset along the beam and leads to the transverse beam centroid oscillation with a spatial-temporal growth. Electron hosing and positron transverse instabilities are likely the biggest obstacles for PWFA (or LWFA) to impact HEP applications. It will cause steering errors as well as limit the energy gain, degrade the beam quality and lead to beam breakup.

How severe is hosing? The coupled equations for beam centroid(xb) and channel centroid (xc) (Whittum et. al. 1991): where Standard theory predics oscillation and exponential growth Asymptotic solution for a linearly tilted beam kbs= kbLpd=(g/2)1/2/e-

Hosing in the blow-out regime Huang et al., Phys. Rev. Lett. Phys. Rev. Lett. 99, 255001 (2007) Parameters: Ipeak = 7.7 kA

Minimal hosing and emittance growth! 25 GeV stages Minimal hosing and emittance growth! 25 GeV Driver 25 GeV Trailing beam 25 GeV Driver 475 GeV Trailing beam np=5.661016cm-3 Ndriver = 4.421010, r= 3 m, L = 58 m, Energy = 25 GeV Ntrailing = 1.71010 , r= 3 m , L = 22 m, Energy = 25 GeV or 475 GeV Rtrans = -Eacc/Edec = 1

Head erosion Matched propagation of beam body: For matched beams head erosion is an issue: Difficult to achieve matched propagation without head erosion for an ordinary beam (i.e., uniform emittance and spotsize). Possible solutions: 1. External focusing 2. Muliple stages such that L of each stage is shorter 3. Trumpet shaped beams that can be produced using a plasma lense. 4. Emittance growth at the head

Beam head erosion in field ionized plasmas

Beam head erosion in field ionized plasmas MM. Zhou, in preparation Slowed down free expansion between A & B (by a factor 0<<1) Vacuum expansion Slower Ionization front Pinch point Ion Focusing

Synchrotron radiation betatron radiation

Ion Motion Ion motion when Matched beam spot size shrinks at large g, low en For future collider eny down by 102 (e.g., 10nm-rad) g up by 10+ nb up by 102 Ion motion must be included in design/models Could cause emittance growth Could cause energy spread Could increase betatron radiation to unacceptable levels Ref. S. Lee et al., AAC Proc (2000); J. Rosenzweig et al., PRL (2006)

Ion Motion Ion motion nb=1.3x1019 nb/n0 m/M=350/1836=.125 np=5.661016cm-3 Ndriver = 4.421010, r= 3 m, L = 58 m, Energy = 250 GeV `nb=1.91x1019 Ntrailing = 1.71010 , r= 3 m , L = 22 m, Energy = 250 GeV nb=1.41x1019 Rtrans = Eloaded/Edec = 1 Ion motion

Positron Acceleration 3-D QuickPIC Simulations, plasma e- density • “Uniform” focusing force (r,z) • Non-uniform focusing force (r,z) Smaller accelerating force Ref. S. Lee et al., Phys. Rev. E (2000); M. Zhou, PhD Thesis (2008)

Positron acceleration Head erosion 5.7GeV in 39cm Evolution of a positron beam/wakefiled and final energy gain in a field-ionized plasma

Positron Acceleration: Needed for e-e+ collider Only at FACET A few scenarios Positrons are accelerated on a positron wake Hollow channels might be needed Use linear wakes Positrons are accelerated on an electron wake One idea for injecting positrons onto an electron wake will be discussed in Mark Hogan’s talk Beam loading by narrow intense positron bunches has not been tackled theoretically as of yet Ref. S. Lee et al., Phys. Rev. E (2000); M. Zhou, PhD Thesis (2008)

Summary Recent success is very promising experiments theory simulation (PIC and reduced PIC) No known show stoppers to extending plasma accelerators to the energy frontier Many questions remain to be addressed for realizing a collider Experiments Theory simulation FACET-class facility is needed to address them Lower energy beam facilities cannot access critical issues in the regime of interest FACET can address most issues of one stage of a 5-20 stage e-e+ TeV collider But by far the most demanding requirements on accels are for HEP HE -- at least 125 GeV on 125 GeV to discover the Higgs

25 GeV Stage No energy spread 25 GeV Driver 25 GeV Trailing beam he ion motion run has the same parameters as the 25gev run except the initial energy of 250GeV. The run was done with 2048x2048x256 cells, and with 0.01 c/wp resolution in transverse direction and 0.047 c/wp in the longitudinal direction. 4 particle/cell is used. The max compression is 217 n_p, the second plot in that slides is actually blown up from the first plot. 25 GeV Driver 25 GeV Trailing beam 25 GeV Driver 475 GeV Trailing beam np=5.661016cm-3 Ndriver = 4.421010, r= 3 m, L = 58 m, Energy = 25 GeV Ntrailing = 1.71010 , r= 3 m , L = 22 m, Energy = 25 GeV or 475 GeV Rtrans = -Eacc/Edec = 1